Question

If the straight line passing through the points $(h,3)$ and $(4,1)$ intersects the line $7x-9y-19=0$ at right angle, then find the value of $h$.

• A. $h=\frac{22}{9}$
• B. $h=\frac{26}{9}$
• C. $h=\frac{22}{2}$
• D. None of these

Answer 1

The correct option is A $h=\frac{22}{9}$

Consider the given points.

$(h,3)$ and $(4,1)$

Slope of the line

$m_1=\frac{1-3}{4-h}$

$m_1=\frac{-2}{4-h}$

Since, the given line

$7x-9y=19$

Slope of the line

$m_2=-\frac{7}{-9}=\frac{7}{9}$

Since, both lines are intersects at right angle.

$m_1.m_2=-1$

So,

$\frac{-2}{4-h}\times \frac{7}{9}=-1$

$\frac{14}{4-h}=9$

$14=36-9h$

$9h=22$

$h=\frac{22}{9}$

Hence, this is the answer.